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  • If A is square matrix such that A = A, then (I + A)3 - 7 A is equal to (A) A (B) I - A (C) I (D) 3A

Q15.    If A is square matrix such that A^{2}=A, then (I + A)^3 - 7 A is equal to

            (A) A
            (B) I – A
            (C) I
            (D) 3A

Answers (1)

best_answer

A is square matrix such that A^{2}=A

(I + A)^3 - 7 A 

=I^{3}+A^{3}+3I^{2}A+3IA^{2}-7A

=I+A^{2}.A+3A+3A^{2}-7A

=I+A.A+3A+3A-7A             (Replace A^{2}  by A)

=I+A^{2}+6A-7A

=I+A-A

=I

Hence, we have  (I + A)^3 - 7 A=I

Option C is correct.

Posted by

seema garhwal

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